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Simplifying (4x2 + -6x + -54) + (9x2 + 9x) = 0 Reorder the terms: (-54 + -6x + 4x2) + (9x2 + 9x) = 0 Remove parenthesis around (-54 + -6x + 4x2) -54 + -6x + 4x2 + (9x2 + 9x) = 0 Reorder the terms: -54 + -6x + 4x2 + (9x + 9x2) = 0 Remove parenthesis around (9x + 9x2) -54 + -6x + 4x2 + 9x + 9x2 = 0 Reorder the terms: -54 + -6x + 9x + 4x2 + 9x2 = 0 Combine like terms: -6x + 9x = 3x -54 + 3x + 4x2 + 9x2 = 0 Combine like terms: 4x2 + 9x2 = 13x2 -54 + 3x + 13x2 = 0 Solving -54 + 3x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -4.153846154 + 0.2307692308x + x2 = 0 Move the constant term to the right: Add '4.153846154' to each side of the equation. -4.153846154 + 0.2307692308x + 4.153846154 + x2 = 0 + 4.153846154 Reorder the terms: -4.153846154 + 4.153846154 + 0.2307692308x + x2 = 0 + 4.153846154 Combine like terms: -4.153846154 + 4.153846154 = 0.000000000 0.000000000 + 0.2307692308x + x2 = 0 + 4.153846154 0.2307692308x + x2 = 0 + 4.153846154 Combine like terms: 0 + 4.153846154 = 4.153846154 0.2307692308x + x2 = 4.153846154 The x term is 0.2307692308x. Take half its coefficient (0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. 0.2307692308x + 0.01331360947 + x2 = 4.153846154 + 0.01331360947 Reorder the terms: 0.01331360947 + 0.2307692308x + x2 = 4.153846154 + 0.01331360947 Combine like terms: 4.153846154 + 0.01331360947 = 4.16715976347 0.01331360947 + 0.2307692308x + x2 = 4.16715976347 Factor a perfect square on the left side: (x + 0.1153846154)(x + 0.1153846154) = 4.16715976347 Calculate the square root of the right side: 2.041362232 Break this problem into two subproblems by setting (x + 0.1153846154) equal to 2.041362232 and -2.041362232.Subproblem 1
x + 0.1153846154 = 2.041362232 Simplifying x + 0.1153846154 = 2.041362232 Reorder the terms: 0.1153846154 + x = 2.041362232 Solving 0.1153846154 + x = 2.041362232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 2.041362232 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 2.041362232 + -0.1153846154 x = 2.041362232 + -0.1153846154 Combine like terms: 2.041362232 + -0.1153846154 = 1.9259776166 x = 1.9259776166 Simplifying x = 1.9259776166Subproblem 2
x + 0.1153846154 = -2.041362232 Simplifying x + 0.1153846154 = -2.041362232 Reorder the terms: 0.1153846154 + x = -2.041362232 Solving 0.1153846154 + x = -2.041362232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -2.041362232 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -2.041362232 + -0.1153846154 x = -2.041362232 + -0.1153846154 Combine like terms: -2.041362232 + -0.1153846154 = -2.1567468474 x = -2.1567468474 Simplifying x = -2.1567468474Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9259776166, -2.1567468474}
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